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Monday, June 01, 2009

Composition as identity does not entail universalism

In my Contingency of Composition paper, I deny the commonly held claim that composition as identity (CAI) entails universalism about composition. (The entailment is defended by Sider, Merricks, et al.) My basic thought was: CAI says just that a complex object is identical to its parts – that tells us only that when you’ve got a complex object, it is identical to its parts, and this is silent about whether or not for any collection of objects there is such a complex object that they are identical to. If many-one identity makes sense then, prima facie, it makes sense to claim that for some collections of objects there’s a one that they are identical to, and some collections of objects such that there’s no one object that they are identical to. All CAI tells us is that it’s all and only the first collections that compose. To assume that every collection composes is just to assume that for any collection of objects, there’s a one to which they are identical. Why would I accept that if I doubted universalism?

In denying the entailment, I need to respond to an argument that both Sider and Merricks give for it. They argue as follows: Suppose (for reductio) the Xs don’t compose. They could do. Go to the world where they do (w). In w, there’s a one, A, that’s identical to the Xs. Given the necessity of identity, A is actually identical to the Xs. So the Xs actually compose A. Contradiction. Formally:

1) ◊(Xs=A)2) ◊(Xs=A) -> □(Xs=A)3) @(Xs=A)

In my paper I attempted to resist this argument with some pretty tricky moves – and while I still think they’re right, I think I haven’t exactly convinced the world! (See the earlier discussion on this blog) But I think I can actually make the point more simply than I did then.

The argument aims to prove that the Xs are actually identical to A. Thus, there is a one that the Xs are identical to: A. So since to compose is to be identical to a one, the Xs compose. But wait! All the argument shows is that it’s actually true that the Xs are A. Where do we get the claim that there’s a one that the Xs are identical to? This follows, obviously, if A is actually a one. But where does that claim come from? All we know is that A is possibly a one. Ex hypothesi A is a one in the world in which the Xs compose. But we can only conclude that A is actually a one – and hence that there’s a one that the Xs are actually identical to – if we have the assumption that anything that is possibly a one is necessarily a one. But what right do we have to make that assumption? If we’re leaving open the possibility that there’s a many that’s not a one but could be (and at this stage we must, lest we beg the question), we should also leave open the possibility that there’s a many that is a one but might not be. Since the many is the one, this is a one that might not be a one: a one that is a many, but that might have been a mere many – a many that is identical to no one. If the Xs don’t actually compose this is the status we should think A has in the world in which they do compose. So sure A is actually identical to the Xs: but A is actually just a name for the plurality, a plurality that don’t actually compose. A is only a one in the worlds in which that many do compose. And we’ve been given no reason to think we’re forced into thinking that our world is one of those.

19 comments:

I'm kind of not tracking the Ted/Trenton argument. In the informal version of it you *say* it uses the necessity of identity. But the relevant principle isn't what I think of as the necessity of identity (i.e. that if a=b then it's necessary that a=b). What we've got is the principle that if its possible that a=b then its necessary that a=b.

Now, I can see how we might argue for this principle if we're restricting our attention to actually existing things. That is, I can see how we can argue for the principle for those rigid designators that actually designate. But what I'm not seeing is how we're supposed to be able to appeal to this principle given that we've assumed that A -- the thing that the Xs compose at w -- doesn't even exist at the actual world.

To put the point otherwise, it seems like all we can get out of the argument is that the Xs are identical to A if A exists. But I thought we were assuming that A doesn't exist?

Thanks Rich. So in the earlier paper I make some water of what happens given the existence is contingent, and I claimed there that the argument can only show that the Xs are A in every world in which A exists, but whether A does is exactly what's up for issue. I still think that's right, but I think what I say here makes that superfluous.

But if I understand you right, you're making a different point: that there's a problem for the actualist in getting from possible identities to necessary identities, because they can't name the mere possibilia?

I take it the argument is fine if you're a possibilist: let 'A' name that thing you believe in that is what the Xs would compose were they to - or an arbitrary such fusion, if there's more than one thing they might compose. Agreed?

If I've got you right - that might be right, in which case: just another problem for the argument! Think of me as offering a response to the argument as put forward by the possibilist, then.

Although let me ask, Rich, do you think something like Kripke's argument for the essentiality of origin fails for the same reason: Kripke asks you to consider a merely possible table that could be made, and gives it a name, and uses the possibility of distinctness to argue for actual distinctness. I get the feeling it's too quick to object to his naming a merely possible object. But am I misunderstanding what you were objecting to about the Sider/Merricks argument?

I can't remember exactly how the Kripke argument goes -- but I'm not sure how we can get the conclusion of actual distinctness rather than the conditional conclusion beginning if the table exists...In general, I've got no problem with actualists "naming merely possible objects" -- though strictly speaking the actualist doesn't believe in mere possibilia so it's going to be naming the surrogates (either the contingently non-concrete objects, or the uninstantiated essences, or whatever). What i'm struggling with is how we go from "possibly a=b" to "a=b" when we're not assuming that 'a' and 'b' actually exist.

So I think I'm just having exactly the same thought as you when you write "the argument can only show that the Xs are A in every world in which A exists, but whether A does is exactly what's up for issue". To my mind that sounds totally right, whether we're actualist or not.

Whilst I'm here, I really ought to ask something about the thing you wrote today. Does this sum it up: in the argument, 'A' is introduced as a name for whatever is identical to the Xs in the world where the Xs the compose. In that world, the Xs compose, which by COI means that 'A' refers to that composite object. But in the actual world, the Xs don't compose, which means that the only thing that 'A' can refer to is the plurality.

So we could see things as a dilemma. Either (i) 'A' is a name for the composite object which the Xs compose at w or (ii) 'A' is a name for whatever is identical to the Xs.

In case (i) we can't conclude that the Xs are actually identical to A since it's an open question whether A exists ('A' might be an empty name in @).

In case (ii) we can't conclude that the Xs compose since its an open question whether 'A' actually refers to a composite object. ('A' might only refer to the Xs in @).

One thing about (ii) is that it seems like we're not reading 'A' as a rigid designator. And that looks to be required for the Kripke style argument. But it's not that 'A' picks out different things in different worlds -- it always picks out the Xs. But in w (and not @) it picks out the composite objects aswell.

If the previous post is right, then one diagnosis that we might give of where the argument goes wrong is this: the argument equivocates between treating 'A' as a rigid designator (which is needed for the appeal to the nec. of identity) and treating 'A' is a non-rigid designator (which gives us the actual existence of A). The response is that Ted and Trenton can't have it both ways.

So my thought was that 'A' is a rigid designator, but it designates something which is contingently a single object rather than a plurality of objects.

It sounds like we agree about the worry about conditionalising on existence. But I've found this doesn't convince everyone, which is why I'm going for the other response here. People have tended to respond as follows. In w, A=Xs. Identity is necessarily necessary, so in w A is necessarily the Xs. Now of course, we might be dealing with a contingent existent, so we don't get that A=Xs in *every* world. But what we do know is that A=Xs in every world in which A or the Xs exist(s). It can't be the case that there's a world with the Xs but not A, because then A and the Xs are distinct (in w) because the Xs has a property A lacks: possibly existing without A. So since the Xs actually exist, A is actually the Xs.

Earlier, I got off the board at the claim that there can't be a world with the Xs but not A. But the point of the current proposal is basically to provide a way of resisting the argument even if you don't get off the board there. A might actually exist. And that's not to say merely that 'A' might actually refer - I mean, the very thing that is A in w might actually exist. And this thing is actually identical to the Xs. But the argument fails because we've not got any reason to hold that this thing is actually a single thing: the very thing that is a single thing in w might actually be merely a plurality of objects. And the thought is that this doesn't mean 'A' is not a rigid designator - that would only follow if ones are essentially ones. But given that we're assuming that mere pluralities are not essentially mere pluralities, I don't see any reason to accept that.

I'm worried about the suggestion that A is / might be 'a name for a plurality' and does not denote 'a one'.

There are plural noun phrases, such as 'the Fs' and there are singular ones, such as 'Socrates', or 'the F'. The former plurally refer to some objects (if all goes well), the latter singularly refer to one object (if all goes well). In the Sider/Merricks argument, A is a singular term: if it denotes, it singularly denotes, and thus denotes exactly one object.

It's problematic to say that a term denotes a plurality. Taking the grammar at face value, that implies that there is such a thing as a plurality. Usually, when people use the term 'plurality', it's on the understanding that the use of that term is strictly speaking inadequate. Strictly speaking, they should use a plural phrase, but since that often requires very awkward wording, they use 'plurality' as a shortcut, which is unproblematic as longs as one keeps in mind that it's strictly speaking inadequate.

The point is, you seem to equivocate between a strict reading of 'plurality' and the one on which it is a slightly lazy form of talking. Only on the latter is a plurality not a one, only on the former is it strictly correct to say of some (singular) term that it denotes a plurality.

What you should say about A, it seems to me, is not that it denotes a plurality but that it plurally denotes some things (plural quantification!). But that's just not true in the Sider/Merricks argument, where it is clear that A is intended to be a singular term, which does not plurally denote.

Grant that 'A' is a singular term in w. I'm thinking Merricks/Sider can't insist that it's actually a singular term without begging the question. This doesn't mean it's not a rigid designator. To be a rigid designator, it merely has to designate the same in every world in which it designates. But if we're taking many-one identity seriously, then there can be a many in w that's identical to a one in v. So a rigid designator can name the many in w and not name any one in w but name the one in v.

I agree we end up saying things that sound odd grammatically - but I think that's just par for the course when we're dealing with CAI. If the many is the one, we need to be able to talk about the plurality that is neither simply a lazy way of talking nor disguised plural reference. We just can't take the grammar at face value if CAI is true.

Let's be netural about terminology and abandon talk about 'singular' or 'plural' reference, since the CAIer thinks there are terms which both singularly and plurally refer, since there are manys that are ones. My point is just that we can name some many that is a one, and that *that very thing* - also *those very things* - might have been a many but not a one. Nothing about CAI rules that out, I think. And it's an ontological claim, so I don't think considerations about grammar *could* rule it out.

So here's something that's come out of a conversation I've been having with Rich. Rich was worried that Kripkean essentialists would object to my talk of a one possibly not being a one. I say 'Necessarily, A=Xs, but that doesn't mean the Xs are necessarily one, because A might not be a one' and Rich thought this is a bit like saying 'Necessarily, water is H2O, but that doesn't mean that water necessarily contains Hydrogen, because H2O might not essentially be a Hydrogen-containing complex'.

Rich is right - it *is* a bit like saying that. But remember, I'm not *accepting* the anti-essentialist claim that a one might not be a one, merely asserting the conditional that one should accept this anti-essentialist claim if one also accepts the anti-essentialist claim that a mere many might not have been a mere many.

Suppose one thought that a particular hydrogen atom, H, could be a molecule containing two hydrogen atoms and an oxygen atom. Maybe an odd anti-essentialist claim to hold, but one could hold it: and it'd be odd to hold this but insist that a particular molecule must be a molecule and couldn't be an atom. Be essentialist in both cases or anti-essentialist in both cases!

The same goes, I think, when it comes to ones and manys. Either hold that it's essential to every one that it is a one and essential to every mere many that it is a mere many, or hold both that there are mere manys that could be ones and that there are ones that could be mere manys.

My objection to the argument from CAI to universalism is that its proponent is doing something odd dialectically: we're starting from the assumption that there are mere manys that could be ones but denying, within the scope of that assumption, that there can be ones that could be mere manys. I can stay silent on whether the essentialist or anti-essentialist route is right: but I think we should be anti-essentialist in both cases or essentialist in both cases, and so either the argument has a false assumption (that the things which don't compose could) or its conclusion doesn't get what is needed (that the many are actually a one). either way, then, the argument fails.

If we’re leaving open the possibility that there’s a many that’s not a one but could be (and at this stage we must, lest we beg the question), we should also leave open the possibility that there’s a many that is a one but might not beI guess you'd have to be leaving open the epistemic possibility, yes? But in that case, you're holding that (2) is not apriori, since you are affirming its antecedent and denying its consequent. But (2) is apriori, or sure seems so. So you could take the Merricks/Sider argument to be (non-circularly) pointing up that the problem for your position is that (2) is apriori.

What is (2)? I can't see any conditionals, so I'm a little confused as to the talk of affirming consequents etc.

Here are two non-conditional claims (this might be what you had in mind, let me know if not):

(1) There's a collection of things, the Xs, such that there's no one thing that is identical to the Xs, but it's metaphysically possible that there's some one thing that is identical to the Xs.

(2) There's a collection of things, the Ys, such that there is one thing that is identical to the Ys, but it's metaphysically possible that there's no one thing that is identical to the Ys.

The argument from CAI to universalism requires us to reject (the metaphysical possibility of) (2) whilst under the assumption that (1) is true. I think that makes the argument bad, because I think (1) and (2) are equally good and should stand or fall together.

Is it that you think (2) is a priori false but not (1)? I would need convincing of that - I don't see any difference between them.

(Also, remember that the argument that (2) is a priori false but (1) isn't must use reasoning that is acceptable to the CAI theorist. A large part of my problem with the Merricks argument is basically that it reasons in a way that I think *is* actually valid, but that we *shouldn't* think is valid on the assumption that composition is identity. If that's right, it's a bad argument, since it's aimed at establishing what follows from CAI.)

The thought would be that you're affirming the antecedent since you're leaving open possibility that there’s a many that’s not a one but could be but you're denying the consequent because you're also leaving open the possibility that there’s a many that is a one but might not be.

That's a better interpretation than mine, Rich: Mike - sorry if I was totally misinterpreting you! Let us know if Rich has got your point right.

But yeah, I agree with Rich that if this is what you meant, I reject the accusation that I deny (2). I affirm both the antecedent and the consequent. In denying that the Xs are necessarily a one, I'm precisely *not* denying that they are necessarily identical to A, just denying that A is necessarily a single entity. Rather, it's a single entity and also a plurality of entities that might just have been a plurality of entities and not a single entity.

One philosopher's MP is another's MT. Once I accept the supposition for reductio and 2, I have ~◊(Xs=A). Right? In other words, why should the Anti-Universalist accept 1 given his belief in the necessity of identity and the failure of the Xs to meet his definition of composition? I wouldn't worry about leaving open the possibility that there is a many that is not a one but could be: that seems tantamount to denying the necessity of identity

"Once I accept the supposition for reductio and 2, I have ~◊(Xs=A). Right?" No. The supposition for reductio is that the Xs don't compose, which entails just that there's no one that the Xs are identical to. To get ~◊(Xs=A) from that and (2) we need to add a premise that says that if it's possible that the Xs are identical to a single thing then if the Xs are identical to anything they are identical to a single thing. But my point was precisely to deny that.

(Of course, I agree that another way to resist the argument is just to deny (1). We can always deny a premise to resist the conclusion - but I wanted to make the stronger claim that one can accept the premises and still resist the conclusion.)

You are a Compositionalist, right? The Xs, in your example do not actually compose A, that is to say, on your view, they are not actually identical to A. But identity is necessary. Thus, there is no possible world in which the Xs compose/are A. QED. Maybe what I have going here is a reductio against Compositionalism, since it seems that composition isn't necessary, unlike identity. The 2 legs and the top do not compose the table but would if assembled properly. But if they are, when assembled, identical to it, then there should be no possible world in which they are distinct.

"The Xs, in your example do not actually compose A, that is to say, on your view, they are not actually identical to A." No: the whole point of the original post is to block that move - to allow that the Xs can be actually identical to A without admitting that they actually compose, by claiming that 'A' actually names a mere plurality of things, and no one thing.

In the normal run of things, we'd be able to reason as follows of course: 'A' is a rigid designator, so if it names something that is identical to some one thing in w then it names something that is identical to some one thing (indeed, that very same thing) in every world in which it names anything at all.

But that reasoning is only good if there *can't* be many-one identities, and so the CAI theorist can't reason that way. If there can be true many one identity claims, I don't see why such claims can't hold across worlds as well as within worlds.

So the Xs in @ might be identical to the single thing A in w. By the necessity of identity, this entails that the Xs are actually identical to A. But I say it *doesn't* entail that A is actually a single thing - A might actually name a mere plurality. So 'A' is actually a mere plurally referring term but in w acts like a singular term - but this doesn't mean 'A' is not a rigid designator: this is just one of those weird many-one identities we've been told make sense!

I do not know if you made any distinction between identity of being or thing of itself and of others.

So i can always say 'i' am always 'i'. Their cannot be two 'i's of me. But when i look at the identity of matter outside of me (things which i think are not me)i first differinate the things from other things and thereby give it 'some' identity. But i am not always so sure of this identity given by me to matters other than me (singularity of identity) as i am of my own self.